MUSCL scheme: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Dthomsen8
m clean up, typo(s) fixed: lmiter → limiter, , → , using AWB
en>Hanyu Ye
The full name of MUSCL has been corrected according to van Leer's original paper.
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
In [[continuum mechanics]], a '''hydrostatic stress''' is an [[isotropic]] [[Stress (mechanics)|stress]] that is given by the weight of water above a certain point. It is often used interchangeably with "[[pressure]]" and is also known as confining stress, particularly in the field geomechanics. Its magnitude <math>\sigma_h</math> can be given by:
The title of the author is Jayson. What me and my family members adore is bungee jumping but I've been taking on new issues lately. I've always loved residing in Kentucky but now I'm contemplating other choices. She functions as a journey agent but soon she'll be on her own.<br><br>psychic readers ([http://formalarmour.com/index.php?do=/profile-26947/info/ http://formalarmour.com/index.php?do=/profile-26947/info]) Feel free to visit my homepage :: [http://kard.dk/?p=24252 real psychic readings] phone readings ([http://www.prayerarmor.com/uncategorized/dont-know-which-kind-of-hobby-to-take-up-read-the-following-tips/ Suggested Reading])
 
:<math>\sigma_h = \displaystyle\sum_{i=1}^n \rho_i g h_i</math>
 
where <math>i</math> is an index denoting each distinct layer of material above the point of interest, <math>\rho_i</math> is the [[density]] of each layer, <math>g</math> is the [[gravitational acceleration]] (assumed constant here; this can be substituted with any [[acceleration]] that is important in defining [[weight]]), and <math>h_i</math> is the height (or thickness) of each given layer of material. For example, the magnitude of the hydrostatic stress felt at a point under ten meters of fresh water would be
 
:<math>\sigma_{h,sand} = \rho_w g h_w = 1000 \,\text{kg/m}^3 \cdot 9.8 \,\text{m/s}^2 \cdot 10 \,\text{m} = 9.8 \cdot {10^4} {kg/ms^2} = 9.8 \cdot 10^4 {N/m^2} </math>
 
where the index <math>w</math> indicates "water".
 
Because the hydrostatic stress is isotropic, it acts equally in all directions. In [[tensor]] form, the hydrostatic stress is equal to
 
:<math>\sigma_h \cdot I_3 =
\left[ \begin{array}{ccc}
\sigma_h & 0 & 0 \\
0 & \sigma_h & 0 \\
0 & 0 & \sigma_h \end{array} \right]
</math>
 
where <math>I_3</math> is the 3-by-3 [[identity matrix]].
 
[[Category:Continuum mechanics]]
[[Category:Orientation]]

Latest revision as of 09:44, 20 April 2014

The title of the author is Jayson. What me and my family members adore is bungee jumping but I've been taking on new issues lately. I've always loved residing in Kentucky but now I'm contemplating other choices. She functions as a journey agent but soon she'll be on her own.

psychic readers (http://formalarmour.com/index.php?do=/profile-26947/info) Feel free to visit my homepage :: real psychic readings phone readings (Suggested Reading)

Retrieved from "https://en.formulasearchengine.com/index.php?title=MUSCL_scheme&oldid=249339"